Question: Simplify the following expression: $ a = \dfrac{-3}{-6n + 4} + \dfrac{3}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-3}{-6n + 4} \times \dfrac{7}{7} = \dfrac{-21}{-42n + 28} $ Multiply the second expression by $\dfrac{-6n + 4}{-6n + 4}$ $ \dfrac{3}{7} \times \dfrac{-6n + 4}{-6n + 4} = \dfrac{-18n + 12}{-42n + 28} $ Therefore $ a = \dfrac{-21}{-42n + 28} + \dfrac{-18n + 12}{-42n + 28} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-21 - 18n + 12}{-42n + 28} $ $a = \dfrac{-18n - 9}{-42n + 28}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{18n + 9}{42n - 28}$